A cold rolled steel wire having the following chemical composition expressed in percent by weight, 0.2≤C %≤0.6, 0.5≤Mn %≤1.0, 0.1≤Si≤0.5%, 0.2≤Cr≤1.0%, P≤0.020%, S≤0.015%, N≤0.010%, and optionally not more than 0.07% Al, not more than 0.2% Ni, not more than 0.1% Mo and not more than 0.1% Cu, the balance being iron and the unavoidable impurities due to processing. This wire has a microstructure including bainite and, optionally, up to 35% acicular ferrite and up to 15% pearlite. A fabrication method and flexible conduits for hydrocarbon extraction are also provided.